Two integrable cases of the dynamics of a rigid body in a force field

The rotation of a rigid body about a fixed point in a force field that is more complex than a constant gravitational field is reviewed, and two new integrable cases of physical importance are identified. These cases are (1) the rotation of a rigid body having a constant magnetic moment about a fixed point in homogeneous gravitational and magnetic fields and (2) the rotation of a rigid body about a fixed center of mass in the gravitational field of an object in the case where the size of the body is much smaller than the distance to the object.